"I am willing to move forward with Republicans on banning these bump stocks," Murphy said on CNN's "State of the Union," referring to devices that allow semi-automatic guns to fire hundreds of rounds per minute.

"I think you have to walk before you run."

Murphy said it's an "important moment," adding that the National Rifle Association (NRA) has never been willing to change U.S. gun laws.

"I think they see that they were likely going to lose this fight in Congress and so now they're trying to get it done through administrative action," he said.

"But this is the first time that the gun lobby has shown a willingness to come to the table."

That's partly due to the fact the Americans don't accept continued mass shootings and Congress "doing absolutely nothing," Murphy said.

"But this is a fairly small change," he said.

"And if we really want to have a downward trajectory on the number of mass shootings and the number of gun deaths every single day, you've got to go far beyond just clarifying that people shouldn't have automatic weapons."

Murphy added that one of the "traps" the gun lobby is setting is only talking about a legislative solution that would have prevented the most recent mass shooting.

The mass shootings get all of the attention, Murphy said, but he added the U.S. has an unparalleled level of daily gun violence.

"And we have a responsibility to address all of that as well," he said.

Background checks, Murphy said, should be the government's next step.

The NRA last week called for additional regulations on bump stocks in the wake of the deadliest mass shooting in modern U.S. history.

Their statement came as many lawmakers have renewed their push for gun control in the wake of the Las Vegas mass shooting.